61.17 Example of DCE Functions

We take the first example presentation above, run it and demonstrate the above functions on the result.

    gap> k := S5Pres.groupK;;
    gap> c := S5Pres.gens[1].name;;
    gap> d := S5Pres.gens[2].name;;
    gap> u := DCE(S5Pres);
    #I Set up generators and inverses
    #I Set up column structure: 4 columns
    #I Pre-processed relators
    #I Done subgroup generators
    #I Also done relators in subgroup
    #I Pushing at weight 3
    #I      1 double 1 single 1 blanks
    #I 1 DCEWord(K,[c, d])^3
    #I   1 cases
    #I 1 DCEWord(K,[(2,3), c])^3
    #I   1 cases
    #I Pushing at weight 5
    #I      3 double 5 single 1 blanks
    #I 2 DCEWord(K,[c, d])^3
    #I   1 cases
    #I 2 DCEWord(K,[(2,3), c])^3
    #I   1 cases
    #I 3 DCEWord(K,[c, d])^3
    #I   2 cases
    #I 3 DCEWord(K,[(2,3), c])^3
    #I   3 cases
    #I Pushing at weight 101
    #I      3 double 5 single 0 blanks
    #I 1 DCEWord(K,[c, c])
    #I   1 cases
    #I 1 DCEWord(K,[d, d])
    #I   1 cases
    #I Pushing at weight 103
    #I      3 double 5 single 0 blanks
    #I 2 DCEWord(K,[c, c])
    #I   1 cases
    #I 2 DCEWord(K,[d, d])
    #I   1 cases
    #I 3 DCEWord(K,[c, c])
    #I   2 cases
    #I 3 DCEWord(K,[d, d])
    #I   1 cases
    << Double coset table "No name" closed 3 double 5 single >>
    gap> u.degree;
    5
    gap> u.status;
    "closed"
    gap> u.dcct;
    3
    gap> a1 := DCEWord(k,(1,2));
    DCEWord(K,[(1,2)])
    gap> b1 := DCEWord(k,(2,3));
    DCEWord(K,[(2,3)])
    gap> c1 := DCEWord(k,c);
    DCEWord(K,[c])
    gap> d1 := DCEWord(k,d);
    DCEWord(K,[d])
    gap> DCEPerm(u,a1);
    #I Starting To Add Cosets
    #I Done cosets, starting image
    (4,5)
    gap> DCEPerm(u,a1*c1*b1);
    #I Done cosets, starting image
    (2,4,5,3)
    gap> DCEPerms(u);
    #I Done cosets, starting image
    #I Done cosets, starting image
    #I Done cosets, starting image
    #I Done cosets, starting image
    [ (2,3), (1,2), (3,5), (3,4) ]
    gap> DCEWrite(u,"s5.dct");
    gap> u1 := DCESetup(S5Pres);
    #I Set up generators and inverses
    #I Set up column structure: 4 columns
    #I Pre-processed relators
    << Double coset table "No name" Set up >>
    gap> DCERead(u1,"s5.dct");
    #I Read the file
    gap> u1;
    << Double coset table "No name" closed 3 double 5 single >>
    gap> DCEPerms(u1);
    #I Starting To Add Cosets
    #I Done cosets, starting image
    #I Done cosets, starting image
    #I Done cosets, starting image
    #I Done cosets, starting image
    [ (2,3), (1,2), (3,5), (3,4) ]

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